Sequences & Series Questions and Answers

Evaluate the expression for x = 4.2. Write your answer in simplest form. (-x + 2)/(x - 5) = ________

Consider the explicit formula for an arithmetic sequence. an = 8n +3 What is the recursive rule for this formula? A. an=a(n-1) +3 and a₁=11 B. an=a(n-1) + 8 and a₁=11 C. an=a(n-1) +3 and a₁=8 D. an =a(n-1) +8 and a₁=3

Saul reads every week. In his first week of reading, he read 50 pages. Each week after that, he read 65 pages. Which expression represents the total number of pages Saul has read, where to represents the number of weeks since he first started reading. 65w + 15 50+65w 65w-15 50+65 + w

Find the 200th term of the following arithmetic sequence. -3, 4, 11, 18, 25, ... Type your answer below. a₂₀₀=

Solve the equation [9]₁₇ X+ [4]₁₇ = [6]₁₇ X + [8]₁₇ for XE Z₁₇. Write your answer as X = [x]₁₇ where 0 ≤ x < 17. What is x?

Find the domain of f(x) =√x+7/x-2 Using interval notation.

The length of a rectangle is 5 more than twice the width. The perimeter is 172 meters. Find the length and width. Width = Length =

A savings account pays a 3% nominal annual interest rate and has a balance of $1,000. Any interest earned is deposited into the account and no further deposits or withdrawals are made. 1). Write an expression that represents the balance in one year if interest is compounded annually. 2). If interest is compounded semi-annually (every six months), what interest rate would be used for each calculation? 3). If interest is compounded semi-annually, which expression represents the account balance in t years? a). 1,000 (1+0.015)^t b). 1,000((1 +0.015)²)^t c). 1,000((1 +0.015)^6)^t d). 1,000((1 +0.03)²)^t ⠀

Drag the tiles to the correct locations on the equation. Not all pieces will be used. Consider this absolute value function. f(x) = |x + 3| How can function f be rewritten as a piecewise function? -x + 3 x < -3 x ≥ 3 -x -3 x - 3 x ≥ -3 x < 3 f(x) = x+3

(v^2/7)/v^2/3 Write your answer using only a positive exponent? Assume that the variable represents a positive real number.

(S → P) Premise (~P v O) Premise (O →G) Premise Conclusion: ((S v D) → G)

Consider the belief network on the right. 1. Write down a Markov network of p(x1, x2, 3). 2. Is your Markov network a perfect map of p(x1, x2, x3) ?

A small printing company launched an online ordering system to expand its business. The equation c = 400*(1.03)^m represents the number of customers c it has in terms of the number of months m since it launched the ordering system. 1. By what factor does the number of customers grow in one year? Write your answer as an expression and a numerical value. 2. If y is time in years, write an equation for the number of customers c as a function of the number of years y after the introduction of the ordering system. 3. If this model continues to apply for a decade, by what factor will the number of customers grow in one decade?

A sample of metal alloy weighs 45.20 g. A student places the sample into a graduated cylinder containing water. The liquid water level rises from 55.0 mL to 80.4 mL. Please include units in your answers. (a) What is the density of the sample of metal alloy? (b) How many kilograms of the metal alloy would fill a 50. L bucket?

Select the correct location on the image. Marta simplified this expression. 4 log5 x + log5 2x - log5 3x In which step did she incorrectly apply a property of logarithms? 4 log5 x + log5 2x - log5 3x Step 1 = log5 4x + log5 2x - log5 3x Step 2 = log5 8x² - log55 3x Step 3 = log5 (8x² / 3x) Step 4 = log5 (8/3)x

A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the box ? You need ( _____ ) in.² of paper to cover the box.

Sketch the solution to each system of inequalities. y > -1x/2 + 2 y < 3x/2 - 2

Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs. Enclose arguments of functions in parentheses and include a multiplication sign between terms. For example, c* In (h).

Neal buys a board game. He pays for the board game and pays $1.54 in sales tax. The sales tax rate is 5.5%. What is the original price of the board game, before tax?

Find and graph the inverse of the function f(x) = x² - 4 for x < 0. f-¹(x) =

Robert climbed 775 steps in 12(1/2) minutes. How many steps did he average per minute?

Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify either the common ratio or the common difference. 7, 9, 10, 12,.... (a) neither (b) geometric; r = 1/2 (c) arithmetic; d = 2 (d) geometric; r = 2

Find all the values of k so that the quadratic expression factors into two binomials. Explain the process used to find the values. 3x² + kx - 8

Which of the following real numbers are constructible: (a) ⁴√5 + ⁸√7. (b) 1/7(4+⁵√3).

A vehicle purchased for $32500 depreciates at a constant rate of 5% per year. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole number.

What is a, the initial amount, for the function: f (x) = 300 (1.16)ˣ? The Compound Interest Formula A = P(1+r/n)ⁿᵗ 1. 300 2. .16 3. x 4. 1.16

Which function defines (9. f)(*) f(1) = log(51) g(x) = 5x + 4 A (g)(1) = 5x log(5x) + 4log(51) B. (g f)(x) = 5x log(5x) + 4 C. (g. f)(x) = 5x - 4 - log(5x) D. (g-f)(x) = 5x + 4 + log(51)

Consider this absolute value function. fi=) = |x + 3| If function fis written as a piecewise function, which piece will it include? A. x+3, x>-3 B= x+3, x>3 C. -x+3, x<-3 D. -x+--3, x<3

Solve the equation [6]17 X+ [10117= [13]17 X+ [7]17 for X Z17. Write your answer as X=[x]17 where 0 sx< 17. What is x?

Evaluate A = P (1+r)ᵗ/(1+r)² Click on the given link to view the question. Evaluate A when P = $9000, r = 0.05, t = 6 years.

Handsome Jack is buying a pony made of diamonds. The price of the pony is P dollars, and Jack also has to pay a 25% diamond pony tax. Which of the following expressions could represent how much Jack pays in total for the pony? Choose 2 answers: A) P + 1/4 B) P + 0.25P C) (P + 1/4)^P D) (5/4)P E) 0.25P

Given f (x): = x² + 3x - 4. Name the vertex 1. (-1.5, -6.25) 2. (-1,7) 3. (-4,0) 4. (-4,1)

Jovie is maintaining a camp fire. She has kept the fire steadily burning for 10 hours with 15 logs. She wants to know how many hours (h) she could have kept the fire going with 9 logs. She assumes all logs are the same. How many hours can Jovie keep the fire going with 9 logs?

Imagine a scatter plot was created based on the data in this table. Which equation best represents the trend line for the data? a) y=(-3/5)x-12 b) y=(3/5)x-12 c) y=(3/5)x+12 d) y=(-3/5)x+12

Find the final hourly wage if a $11.00 starting wage is increased by 2 % each year for 8 years. The final wage is $. round answer to 2 decimal places

Two angles of a triangle have the same measure and the third one is 57 degrees greater than the measure of each of the other two. Find the measure of the LARGEST angle in the triangle.

A store has a 40% off sale on headphones. With this discount, the price of one pair of headphones is $36. What is the original price of the pair of headphones?

The count in a bacteria culture was 200 after 10 minutes and 1600 after 40 minutes. Assuming the count grows exponentially, What was the initial size of the culture? _____ Find the doubling period. _____ Find the population after 115 minutes. _____ When will the population reach 10000. _____ You may enter the exact value or round to 2 decimal places.

Kathryn left the restaurant traveling 16 mph. Then, 3 hours later, Samantha left traveling the same direction at 28 mph. How long until Samantha catches up with Kathryn?

Tatiana is asked about her age. She answers as follows. "My age is 2 more than four times the age of my son. The sum of our ages is 87.

Find the twenty-seventh term of the arithmetic sequence 22, 21, 20, ... a₂₇ = (Simplify your answer.)

An endangered species of sparrow had an estimated population of 848 in 2000, and scientists predict that its population will decrease by half each year. Estimate the population in 2004. Estimate the year the sparrow will be extinct. Estimate the population in 2004. Estimate the year the sparrow will be extinct. (Round up to the nearest year.)

After a 10% reduction, you purchase a new digital player for $292.5. What was the price of the digital player before the reduction? A) First write an equation you can use to answer this question. Use x as your variable and express any percents in decimal form in the equation. B) Solve your equation in part [A] to find the original price of the digital player. Answer: The original price of the digital player was dollars.

Find three consecutive numbers whose sum is 327. smaller number = middle number = larger number =

The temperature inside of a storage building, in degrees Fahrenheit, can be modeled using the equation F(t) = -8.3 cos{(π/5)t} + 63.7, where t is the number of hours since midnight. (a) At what temperature is the building at midnight? Explain how you arrived at your answer. (b) How many hours after midnight does it take for the temperature to first reach its maximum value? Explain.

Dilate the following figures with the given center of dilation and scale factor, k: (a)D(-₇,₂),₂ center of dilation (-7,2) k=2

Classify the model as exponential growth or decay: A = 1200 (.85)⁶

Find the first term of the arithmetic sequence with a6 = 2.7 and a7 Find the first term of the arithmetic sequence with an = 2.7 and an = 5.2 Answer: How many integers between 65/9 and 2024/9 are exactly divisible by 7? Answer: Find the 6th term of a geometric progression whose 2nd term is -2 and the common ratio is 2. Answer: Insert 3 arithmetic means between 25 and 31. (Use decimal representation instead of fraction) Answer:

Describe how the relationship between volume of a pyramid and volume of a rectangular prism is similar to the relationship between the volume of a cylinder and the volume of a cone.

A coordinate plane is formed by two intersecting number lines. The horizontal line is called the x-axis. The vertical line is called the y-axis. This two-axis system is called the coordinate system The coordinates of a point are Quadrant II represented by the ordered pair (x, y). This shows the distance the point is from the origin (0, 0), in the domain (the set of x coordinates) and the range (the set of y coordinates). A set of ordered pairs is called a relation. In the graph at right, Point A is located at (4, 2). Point B is located When two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. The coordinates of Point C differ from the coordinates of Point B by only the sign of the x-coordinate. So Point C, located at (5, -3), is a reflection of Point B across the y-axis. Write the ordered pair for each lettered point on the grid.